Background suppression for MM-wave spectroscopy

ABSTRACT

A system includes first and second gas cells, each comprising a respective sealed interior waveguide. The first gas cell contains a dipolar gas and the second gas cell does not contain a dipolar gas. The system includes first and second transmit antennas coupled to the first and second gas cells, respectively, to provide first and second electromagnetic waves to the interior of the first and second gas cells, respectively; first receive antenna coupled to the first gas cell to generate a first signal indicative of an amount of energy in the first electromagnetic wave after travel through the first gas cell; second receive antenna coupled to the second gas cell to generate a second signal indicative of an amount of energy in the second electromagnetic wave after travel through the second gas cell; processor configured to calculate a background-free signal based on a difference between the first and second signals.

BACKGROUND

This relates generally to spectroscopy, and more particularly to mm-wavespectroscopy.

SUMMARY

In at least one example, a system includes: first and second gas cells,each including a respective sealed interior waveguide. The first gascell contains a dipolar gas and the second gas cell does not contain adipolar gas. The system includes first and second transmit antennascoupled to the first and second gas cells, respectively, to providefirst and second electromagnetic waves to the interior of the first andsecond gas cells, respectively; first receive antenna coupled to thefirst gas cell to generate a first signal indicative of an amount ofenergy in the first electromagnetic wave after travel through the firstgas cell; second receive antenna coupled to the second gas cell togenerate a second signal indicative of an amount of energy in the secondelectromagnetic wave after travel through the second gas cell; processorconfigured to calculate a background-free signal based on a differencebetween the first and second signals.

In another example, a system includes: a first gas cell comprising asealed interior waveguide that contains a dipolar gas; a second gas cellcomprising a sealed interior waveguide that does not contain a dipolargas; a first transmit antenna coupled to the first gas cell andconfigured to provide a first electromagnetic wave to travel in thesealed interior of the first gas cell; a second transmit antenna coupledto the second gas cell and configured to provide a secondelectromagnetic wave to travel in the sealed interior of the second gascell; and an electromagnetic coupler coupled to the gas cells. Theelectromagnetic coupler is configured to receive the first and secondelectromagnetic waves after travel through the first and second gascells, and generate an electromagnetic wave indicative of a differencebetween the received first and second electromagnetic waves.

In yet another example, a method includes: providing a firstelectromagnetic wave to travel in a sealed interior waveguide of a firstgas cell; providing a second electromagnetic wave to travel in a sealedinterior waveguide of a second gas cell; receiving the first and secondelectromagnetic waves after travel through the first and second gascells; and generating a background-free signal based on a differencebetween the first and second electromagnetic waves. The sealed interiorof the first gas cell contains a dipolar gas and the sealed interior ofthe second gas cell does not contain a dipolar gas.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a block diagram of a system for background suppression inaccordance with various examples.

FIG. 2 shows another block diagram of a system for backgroundsuppression in accordance with various examples.

FIGS. 3a-3c show waveforms corresponding to energy absorption as afunction of frequency for different gas cells or combinations thereof inaccordance with various examples.

FIGS. 4a and 4b show various transmitter configurations in accordancewith various examples.

FIGS. 5a and 5b show various electromagnetic couplers in accordance withvarious examples.

FIGS. 6a, 6b, and 6c show various receive antenna configurations inaccordance with various examples.

FIG. 7 shows a flow chart of a method for background suppression inaccordance with various examples.

FIG. 8 shows a block diagram of a system for Doppler-free backgroundsuppression in accordance with various examples.

FIGS. 9a-9c show waveforms corresponding to energy absorption as afunction of frequency for different gas cells or combinations thereof inaccordance with various examples.

FIG. 10 shows a flow chart of a method for Doppler-free backgroundsuppression in accordance with various examples.

DETAILED DESCRIPTION

Stable clock signals, usable as a base frequency source either directly,or converted (e.g., divided down) to some multiple of a base frequencysource, can be generated from various circuits and configurations. Oneexample clock signal that demonstrates long-term stability is an atomicclock, which produces a signal in response to the natural and quantumresponse of atoms or molecules to an excitation source. In one example,such atoms are alkali metals stored in a chamber (e.g., a hermeticchamber), where the excitation source is one or more lasers directed tothe cell and the response of the atoms in the chamber is detected bymeasuring the amount of laser energy (photons) that passes through thechamber as the laser frequency sweeps across a range. In anotherexample, such molecules are dipolar gases also stored in a chamber,where the excitation source is an electromagnetic wave propagatingthrough the chamber and the response of the molecules in the chamber isdetected by measuring the amount of electromagnetic energy that passesthrough the chamber as the frequency of the source sweeps across arange. In the example where the excitation source is a laser, thewavelength of the electromagnetic field is on the order of 800 nm, whichcorresponds to approximately 1.5 eV of energy. However, in the examplewhere the excitation source is a mm-wave source, the wavelength of theelectromagnetic field is on the order of 2 mm, which corresponds toapproximately 0.6 meV of energy.

An atomic clock apparatus may include a sealed chamber (e.g., a gascell) that stores a dipolar gas. The gas cell includes anelectromagnetic entrance into which an electromagnetic wave (or field)enters near a first end of the gas cell and an electromagnetic exit fromwhich an electromagnetic wave exits near a second end of the gas cell.In another example, the electromagnetic wave enters and exits from thesame port (e.g., after reflecting back from the opposite end of the gascell). A transmitter may be coupled to the electromagnetic entrance toprovide the electromagnetic wave to the gas cell, and a receiver may becoupled to the electromagnetic exit to receive the electromagneticenergy that passes through the gas cell. The electromagnetic wave thatexits the gas cell is measured (e.g., by a diode detector) to determinean amount of absorption by (or transmission through) the dipolar gas,with the measure indicative of the quantum response of the gas as afunction of the wave frequency. However, one or more of the transmitter,the receiver, the gas cell itself, and associated circuitry andelectronic devices may add noise to or otherwise color the molecularabsorption signal thus reducing the accuracy in determining the quantumresponse of the gas, and thus the accuracy and stability of the atomicclock.

Examples of this description address the foregoing by providing asimilar electromagnetic wave to two gas cells, where one gas cellcontains a dipolar gas, while the other gas cell does not contain adipolar gas. For example, the gas cell not containing the dipolar gasmay contain atmospheric gas, either at atmospheric pressure or at apressure different than atmospheric pressure. In another example, thegas cell not containing the dipolar gas does not contain any gas (e.g.,is approximately at vacuum). The response of the gas cell not containingthe dipolar gas to electromagnetic wave interrogation is generally abackground frequency response of the system (e.g., due to impacts on thefrequency response observed by a receiver caused by transceivercircuitry, the gas cell itself, and other associated circuitry andelectronic devices). However, the response of the gas cell containingthe dipolar gas to electromagnetic wave interrogation also includes thequantum response of the gas as a function of the wave frequency. The gascells are substantially similar in their physical characteristics, suchas dimensions, shape, manufacturing processes, interior coatings,entry/exit passage construction, and the like, such that the response ofthe gas cell containing the dipolar gas also includes the backgroundresponse in addition to the quantum response of the gas.

The response of the gas cell not containing the dipolar gas issubtracted from the response of the gas cell containing the dipolar gas,which effectively removes the background response and provides abackground-free response. The background-free response can then beutilized by a transceiver to determine the quantum response of the gaswith improved accuracy and stability, without being colored by thebackground frequency response of the various system components. As aresult, the transceiver generates a precision clock signal withincreased accuracy and stability.

FIG. 1 shows a block diagram of a system 100, which in one example is aclock system. The system 100 includes a semiconductor substrate 102including a first gas cell 104 a and a second gas cell 104 b. The firstand second gas cells 104 a, 104 b each include a passage 106 a, 106 b,respectively, which serves as an entrance into the gas cell 104 a, 104b. The first and second gas cells 104 a, 104 b also each include apassage 108 a, 108 b, respectively, which serves as an exit from the gascell 104 a, 104 b. A transceiver 110 is coupled to the gas cells 104 a,104 b. In this example, the transceiver 110 includes a transmitter 112(e.g., a sub-block of transceiver 110) that is configured to provide anelectromagnetic wave to the gas cells 104 a, 104 b by way of theirrespective entry passages 106 a, 106 b. The transceiver 110 alsoincludes a receiver 114 (e.g., a sub-block of transceiver 110) that isconfigured to receive the electromagnetic waves (or signals relatedthereto, such as an analog voltage signal) after travel through the gascells 104 a, 104 b by way of their respective exit passages 108 a, 108b. Although shown schematically as separate blocks for the purpose ofdescribing their functionality, the transmitter 112 and/or the receiver114 may share certain components (e.g., circuitry), at least some ofwhich are described further below.

In this example, the transceiver 110 also includes a processor 116,although in other examples the processor 116 may be a distinct componentrelative to the transceiver 110. In this example, the transmitter 112,the receiver 114, and the processor 116 are coupled, while the processor116 is configured to, among other things, control the transmitter 112 toprovide electromagnetic waves to the gas cells 104 a, 104 b and processsignals received from the gas cells 104 a, 104 b and provide suchprocessed signals to the receiver 114. The transceiver 110 is configuredto provide a stable reference clock signal in response toelectromagnetic interrogation of the first and second gas cells 104 a,104 b, which is described in further detail below. The electricaldipolar nature of dipolar gas provides a detectable response to aninterrogating electromagnetic wave, as further described below.

In one example, the gas cells 104 a, 104 b are formed in connection withan integrated circuit wafer, which can include multiple layers affixedrelative to the semiconductor substrate 102. In FIG. 1, as well as invarious subsequent figures, the shape depicted of the gas cells 104 a,104 b depicts a generally top-down view, such as a planarcross-sectional view parallel to the plane generally defined by thesubstrate 102 in which the gas storage cavities of gas cells 104 a, 104b are formed. Generally, gas cells 104 a, 104 b include a sealedenclosure having an interior in which a gas is stored. Morespecifically, gas cells 104 a, 104 b are configured to store a dipolargas, such as water vapor (H2O), CH3CN, HC3N, OCS, HCN, NH3, and isotopesof these gases, or any other dipolar molecular gas, inside an enclosedcavity of the cell, the cavity being sealed by nature of shapes,layering, and the like relative to the semiconductor substrate 102 andlayers that combine to enclose the dipolar gas at a relatively low(e.g., 0.1 mbar) pressure. In addition, in certain examples, one of thegas cells 104 a, 104 b does not contain a dipolar gas and may insteadcontain atmospheric gas. Further, in some examples, the gas cell 104 a,104 b that does not contain the dipolar gas is not sealed and is insteadleft open to atmosphere. For reasons detailed below, the enclosedpressure of one or both of the gas cells 104 a, 104 b can be other thanthe example provided, as examples described herein afford additionalbeneficial results that are independent of, or minimally affected by,the sealed pressure of the dipolar gas.

In one example, the gas cells 104 a, 104 b also include, or are linedalong most of their interior surfaces with, a material to facilitate theinterior as a signal waveguide, where such material is, for example, aconductor or a dielectric. In an example, the cross-sectional shape ofgas cells 104 a, 104 b is square, rectangular, trapezoidal, or othershapes, while the dimensions of gas cells 104 a, 104 b may vary, wherethe gas cells 104 a, 104 b are 30 to 150 mm long, 1 to 3 mm wide, and0.5 to 1.5 mm tall, where selections of these or comparable sizes matchproperties for efficient wave propagation given the frequency of thedesired wave. Further, while the longitudinal shape is linear in FIG. 1(and other figures), it also may bend or turn so as to form, forexample, a meandering path.

FIG. 2 shows a block diagram of a system 200, which is similar to thesystem 100 described above with regard to FIG. 1. However, in FIG. 2,the transceiver 110 is shown having functional sub-blocks including asignal generator 206, a modulator 208, a loop filter 210, and a lock-inamplifier 212, all of which are described in further detail below. Thesesub-blocks 206-212 support transmitter 112 and/or receiver 114functionality. Additionally, the transceiver 110 is coupled to the entrypassages 106 a, 106 b and configured to provide electromagnetic waves tothe gas cells 104 a, 104 b by way of transmit antennas 202 a, 202 b,respectively. In an example, the transmit antennas 202 a, 202 b receivean analog voltage from the transceiver 110 and, in response to thereceived analog voltage, generate an electromagnetic wave that isprovided to the gas cells 104 a, 104 b, respectively. The transceiver110 is also coupled to the exit passages 108 a, 108 b and configured toreceive the electromagnetic waves after travel through the gas cells 104a, 104 b by way of receive antennas 204 a, 204 b, respectively. Althoughnot shown schematically, in some examples the receive antennas 204 a,204 b include a square-law detector or another type of detector thatproduce an output signal, for example, that is proportional to theintensity or amplitude of the received electromagnetic wave are coupledto the antennas 204 a, 204 b. Thus, in such examples, the receiveantennas 204 a, 204 b receive an electromagnetic wave from the exitpassages 108 a, 108 b and generate an analog voltage based on thereceived electromagnetic wave.

In the example of FIG. 2, the processor 116 processes the signals (e.g.,analog voltages) generated by the receive antennas 204 a, 204 b beforeproviding a resulting signal to the receiver 114 portion of thetransceiver 110. However, as described further below, in other examplesa different electromagnetic coupler resides intermediate to the exitpassages 108 a, 108 b and the receive antennas 204 a, 204 b andgenerates a resulting electromagnetic wave based on the receivedelectromagnetic waves from the exit passages 108 a, 108 b. Althoughshown schematically as separate components, it should be appreciatedthat in some examples the transceiver 110 (or separate transmitters andreceivers, as the case may be) includes (e.g., as integrated devices)the associated antennas 202 a, 202 b, 204 a, 204 b (including square-lawdetectors as described above).

The transmit antennas 202 a, 202 b are positioned proximate the entrypassages 106 a, 106 b, so that electromagnetic energy from thetransceiver 110 may be communicated to the transmit antennas 202 a, 202b and then into the gas cells 104 a, 104 b by way of entry passages 106a, 106 b. As described in further detail below, in one example, aseparate transmitter 112 or transceiver 110 (not shown in FIG. 2 forsimplicity) provides the electromagnetic energy/wave to each of the gascells 104 a, 104 b (e.g., by way of transmit antennas 202 a, 202 b). Inanother example, a single transmitter 112 or transceiver 110 providesthe electromagnetic energy/wave, which is received by a directionalcoupler (not shown in FIG. 2 for simplicity) that generates first andsecond electromagnetic waves to be provided to the first and second gascells 104 a, 104 b, respectively.

In the examples of FIGS. 1 and 2, the term passage in the context of theentry passages 106 a, 106 b and exit passages 108 a, 108 b suggests asignal communications pathway for passage of the electromagnetic signal,but not necessarily an open aperture to ambient per se that otherwisecould cause the sealed dipolar gas in one or both of the gas cells 104a, 104 b to escape. Such a pathway may be formed in various fashions,such as by a glass layer as the upper surface of the sealed enclosure ofthe gas cell and providing an opening in the metal surround that isotherwise formed within the cell—in this manner, an electromagneticsignal may pass through the opening and glass into the interior of thecell, thereby reaching the dipolar gas sealed therein. However, in otherexamples, the one of the gas cells 104 a, 104 b that does not contain adipolar gas is not sealed and thus is open to atmosphere.

The transceiver 110 is both for transmitting (TX) and receiving (RX)signals. The transceiver 110 is generally described by way of examplebut not limitation, for accomplishing the transceiver and signalresponsiveness described herein. In this regard, a signal generator 206is connected, and is modulated by a modulator 208, to provide a basefrequency controlled TX signal that, as detailed later, is swept acrossa particular frequency range from below to past the intrinsic quantumtransition frequency for the dipolar gas in one of the gas cells 104 a,104 b (e.g., 182.427 GHz for OCS). Modulator 208 modulates the frequencyof the interrogation signal provided by the signal generator 206. Themodulation frequency ranges, such as between 10 to 50 KHz.

After the signals pass through the gas cells 104 a, 104 b, they arereceived by the receive antennas 204 a, 204 b, respectively (or otherelectromagnetic coupler as described further below). As described above,the receive antennas 204 a, 204 b generate a signal in response to thereceived electromagnetic wave, such as an analog voltage. The processor116 is coupled to the receive antennas 204 a, 204 b and receives the RXsignal (e.g., analog voltage) from the receive antennas 204 a, 204 b. Insome examples, the processor 116 converts the received analog RX signalto a digital value (e.g., using an integrated analog-to-digital (ADC)converter), while in other examples an external ADC resides intermediateto the receive antennas 204 a, 204 b and the processor 116 to providethe processor 116 with a digital RX signal.

A lock in amplifier 212 in turn receives a signal generated by theprocessor 116 (or other electromagnetic coupler). Particularly, receiveantennas 204 a, 204 b are positioned proximate the exit passages 108 a,108 b of the gas cells 104 a, 104 b, so that electromagnetic energy thattravels through gas cells 104 a, 104 b may be communicated from the exitpassages 108 a, 108 b to receive antennas 204 a, 204 b and then totransceiver 110 by way of the processor 116 and, more particularly, tolock in amplifier 212. Generally, lock in amplifier 212 uses the signalfrom the modulator 208 to measure the processed RX signal from theprocessor 116 (or other electromagnetic coupler) at the same modulationfrequency provided by modulator 208. In this way, lock in amplifier 212is able to reject noise outside the modulation frequency and therebyreduce the noise from the system.

As described in further detail below, in one example, a separate receiveantenna 204 a, 204 b receives the electromagnetic energy/wave aftertravel through each of the gas cells 104 a, 104 b. The receive antennas204 a, 204 b convert the electromagnetic wave into an RX signal, such asan analog voltage, which is further processed by the processor 116before being utilized by the transceiver 110. In another example, anelectromagnetic coupler (not shown in FIG. 2 for simplicity) receivesand processes the electromagnetic energy/waves after travel through eachof the gas cells 104 a, 104 b (e.g., in the electromagnetic domain),while one or more receive antennas receive the resultant processedelectromagnetic wave from the electromagnetic coupler, convert theprocessed electromagnetic wave into an RX signal, such as an analogvoltage, which is utilized by the transceiver 110. These examples aredescribed further below.

In more detail, the TX signal may be a sinusoid, although other periodicoscillating signals also may be used, so long as such signal includes aFourier component in the frequency of interest. The TX signal need notbe continuous and thus in some examples is a discrete signal. The TXsignal is provided to the gas cells 104 a, 104 b. Under feedbackcontrol, signal generator 206 also provides the reference clock REFCLK,which is refined using examples described herein. The RX signal (e.g.,the analog voltage value received by the processor 116 in FIG. 2)represents an amount of the originally transmitted signal TX that passesthrough the gas cells 104 a, 104 b and contains the information of theabsorption of the dipolar gas at the quantum rotations transitionfrequency. In examples of this description, the RX signal from each ofthe gas cells 104 a, 104 b (e.g., by way of receive antennas 204 a, 204b and a square-law detector or similar device) is received by theprocessor 116, which generates a processed RX signal that is provided tothe transceiver 110. In response to the processed RX signal, lock inamplifier 212 provides a signal that is the first derivative of thesignal as it is swept in frequency. Consequently at the frequencycorresponding to the quantum rotational molecular transition, the firstderivative is zero and the error signal ERR is zero. At frequenciesdifferent from the quantum rotational transition, the signal ERR is notzero and provides a correction to the loop filter 210, allowing it to“lock” the clock to the quantum transition frequency. This apparatusalso filters out noise as detected by reference to the modulationfrequency provided by modulator 208. In one example, lock in amplifier212 provides the error signal ERR as an in-phase output, and the errorsignal ERR is used as an input by a loop filter 210 (or controllercircuit) for providing a control output signal CO to signal generator206. As further detailed below, such feedback selectively adjusts the TXoutput signal frequency, following an initial sweep, to ultimatelymaintain this frequency at a peak absorption frequency of the dipolarmolecular gas inside the sealed interior of the gas cell 104 a, 104 bthat contains the dipolar gas, with that maintained frequency providinga stable output reference clock REFCLK. In some examples, the RF powerof the TX and RX loop is controlled so as to avoid or mitigate starkshift effects (frequency shifts in response to quantum transitionproduced by the presence of an electric field).

As described above, one or more of the transmitter 112 and the receiver114 (or transceiver 110), the gas cell 104 itself, and associatedcircuitry and electronic devices may add noise to or otherwise color themolecular absorption signal, thus reducing the accuracy in determiningthe quantum response of the gas, and thus the accuracy of the atomicclock as a precision clock source. Examples of this description addressthe foregoing providing a similar electromagnetic wave to two gas cells104 a, 104 b, where one gas cell contains a dipolar gas (e.g., 104 a),while the other gas cell does not contain a dipolar gas (e.g., 104 b).The response of the gas cell not containing the dipolar gas 104 b toelectromagnetic wave interrogation is generally a background frequencyresponse of the system 200 (e.g., due to impacts on the frequencyresponse observed by a receiver caused by transceiver circuitry 202, thegas cell 104 a, 104 b itself, and other associated circuitry andelectronic devices). However, the response of the gas cell containingthe dipolar gas 104 a to electromagnetic wave interrogation alsoincludes the quantum response of the dipolar gas as a function of thewave frequency. The gas cells are substantially similar in theirphysical characteristics, such as dimensions, shape, manufacturingprocesses, interior coatings, entry/exit passage construction, and thelike, such that the response of the gas cell containing the dipolar gasalso includes the background response in addition to the quantumresponse of the gas.

In examples of this description, the response of the gas cell notcontaining the dipolar gas 104 b is subtracted from the response of thegas cell containing the dipolar gas 104 a (or vice versa), whicheffectively removes the background response and provides abackground-free response, or a processed RX signal, which can then beutilized by the transceiver 110 (e.g., the lock in amplifier 212) todetermine the quantum response of the gas with improved accuracy andstability, without being colored by the background frequency response ofthe various system components. As a result, the transceiver 110generates the precision clock signal REFCLK with increased accuracy andstability. Various examples of this approach are described in furtherdetail below.

Generally, the transceiver 110 is configured to sweep the modulated basefrequency TX signal, such that the base frequency is swept across aninitial frequency range that includes the intrinsic quantum rotationalstate transition frequency for the dipolar gas in the gas cell(s) 104 a,104 b. Thus, in the example where the dipolar gas is OCS, the range willinclude the intrinsic quantum rotational state transition frequency of182.427 GHz for OCS, and could include, for example, a sweep fromapproximately 182.25 GHz to 182.75 GHz.

In a first example, one of the gas cells 104 a is filled with a dipolargas, as described above, while the other of the gas cells 104 b is notfilled with a dipolar gas and may be filled with, for example,atmospheric gas. In another example, the gas cell 104 b not containingthe dipolar gas does not contain any gas (e.g., is approximately atvacuum). Since the gas cell 104 b is not filled with a dipolar gas, theelectromagnetic energy received from the exit passage 108 b by thereceiver 114 or transceiver 110 is indicative of a background signalabsorption or transmission response of the system, which may include oneor more of the transmitter 112 and the receiver 114 (or transceiver110), the gas cell 104 itself, and associated circuitry and electronicdevices such as the processor 116. A signal is generated (e.g., by thereceive antennas 204 a, 204 b along with any intermediate device such asa square-law detector or similar device) that is indicative of thereceived electromagnetic energy.

FIG. 3a shows a waveform 300 of an example background signal generatedby the receive antennas 204 a, 204 b (e.g., by a square-law detector orsimilar device) in response to the electromagnetic energy received fromthe exit passage 108 b of the gas cell 104 b. For example, the waveform300 shows transmission energy as a function of frequency of the receivedelectromagnetic wave. Ideally, the background waveform 300 would beflat, which would indicate that the transmission (or absorption) of thesystem is independent of frequency. However, in real world examples,this is not the case.

FIG. 3b shows a waveform 310 of an example RX energy transmission signalgenerated by the receive antenna 204 a (e.g., by a square-law detectoror similar device) in response to the electromagnetic energy receivedfrom the exit passage 108 a of the gas cell 104 a. For example, thewaveform 400 shows the RX energy transmission through the dipolar gas inthe gas cell 104 a as a function of frequency of the receivedelectromagnetic wave. In various examples, the gas cells 104 a, 104 bare substantially similar in their physical characteristics, such asdimensions, shape, manufacturing processes, interior coatings,entry/exit passage construction, and the like, such that the backgroundresponse for the gas cells 104 a, 104 b is also substantially similar.

FIG. 3c shows a waveform 320 of an example background-free signal thatresults when the background waveform 300 (e.g., obtained from thereceive antenna 204 b coupled to the gas cell 104 b that does notcontain dipolar gas) is subtracted from the waveform 310 that reflectsthe RX energy transmission through the dipolar gas (e.g., obtained fromthe receive antenna 204 a coupled to the gas cell 104 a that containsdipolar gas). In another example, the waveform 310 that reflects the RXenergy transmission through the dipolar gas is instead subtracted fromthe background waveform 300, which has the same effect but with areversal in sign of values.

As described in further detail below, in some examples the processor 116is configured to receive the background signal (e.g., waveform 300) andthe gas transmission signal (e.g., waveform 310) and calculates thedifference represented by the waveform 320. In other examples, anelectromagnetic coupler is coupled to the exit passages 108 a, 108 b andthus receives the electromagnetic waves after travel through the gascells 104 a, 104 b and generates a resulting electromagnetic wave thatis indicative of the difference in the received waves. Thus, thebackground-free waveform 320 represents suppression of the impacts ofgas cell 104 geometry, environment, or surrounding electronics like thetransceiver 110, which increases the accuracy of determining the maximumabsorption frequency and thus the accuracy and stability of the REFCLKsignal that results from such determination.

FIGS. 4a and 4b show examples of different transmitter configurationsfor providing electromagnetic waves to the entry passages 106 a, 106 bof the gas cells 104 a, 104 b. In the example of FIG. 4a , a firsttransmitter 402 a (or a transmit portion of a first transceiver) iscoupled to the entry passage 106 a of the gas cell 104 a (e.g., by firsttransmit antenna 202 a, not shown for simplicity). Similarly, a secondtransmitter 402 b (or a transmit portion of a second transceiver) iscoupled to the entry passage 106 b of the gas cell 104 b (e.g., bysecond transmit antenna 202 b, not shown for simplicity). In the exampleof FIG. 4a , the processor 116 (or other transmitter and/or transceivercircuitry) may be configured to cause the first and second transmitters402 a, 402 b to provide approximately equal electromagnetic waves to thefirst and second gas cells 104 a, 104 b, respectively, such that thebackground response is approximately equal in the RX signals,facilitating elimination of the background response after the differenceis calculated (e.g., by the processor 116 or other coupler, as describedfurther below). In some examples, the electromagnetic waves provided tothe first and second gas cells 104 a, 104 b have the same amplitude andthe same frequency.

In the example of FIG. 4b , a single transmitter 402 (or a transmitportion of a single transceiver) is coupled to a directional coupler404, which is in turn coupled to the entry passages 106 a, 106 b of thegas cells 104 a, 104 b (e.g., by way of first and second transmitantennas 202 a, 202 b, not shown for simplicity). The directionalcoupler 404 is configured to receive an electromagnetic wave from thetransmitter 402 and generate corresponding electromagnetic waves, beingapproximately equal (e.g., by splitting the received electromagneticwave energy), and providing those corresponding, split electromagneticwaves to the gas cells 104 a, 104 b. Similar to the example of FIG. 4a ,since the corresponding electromagnetic waves are approximately equal,the background response is also approximately equal in the RX signals,facilitating elimination of the background response after the differenceis calculated (e.g., by the processor 116 or other coupler, as describedfurther below). In some examples, the electromagnetic waves provided tothe first and second gas cells 104 a, 104 b have the same amplitude andthe same frequency.

As described above, in some examples the processor 116 receives thebackground signal and the gas transmission signal from receive antennas204 a, 204 b, which convert the received electromagnetic wave into, forexample, an analog voltage. In such examples, the processor 116determines a background-free signal based on the background and gastransmission signals. However, in other examples, an electromagneticcoupler receives the electromagnetic waves from the exit passages 108 a,108 b and generates a resultant electromagnetic wave that is the resultof subtracting the background signal from the gas transmission signal,or vice versa. This resultant electromagnetic wave is then converted toan analog voltage, which may optionally be processed (e.g., by theprocessor 116) and otherwise utilized by the transceiver 110 to generatethe precision clock signal REFCLK as described above.

FIG. 5a shows one example of an electromagnetic coupler, which is arat-race coupler 500. The rate race coupler 500 is configured to receiveelectromagnetic waves from the exit passages 108 a, 108 b after travelthrough the gas cells 104 a, 104 b. The rat-race coupler 500 includes afirst input RX1 coupled to the exit passage 108 a of the gas cell 104 aand a second input RX2 coupled to the exit passage 108 b of the gas cell104 b. The rat-race coupler 500 also includes a first output 502 and asecond output 504. In this example, the first output 502 produces anelectromagnetic wave that corresponds to the difference of the firstinput RX1 and the second input RX2 (e.g., RX1−RX2), while the secondoutput 804 produces an electromagnetic wave that corresponds to the sumof the first input RX1 and the second input RX2 (e.g., RX1+RX2).

The first output 502 is coupled to a receive antenna 506, while thesecond output 504 is coupled to a receive antenna 508. The receiveantennas 506, 508 are functionally similar to the receive antennas 204a, 204 b, described above, and thus are configured to produce an outputsignal, for example, that is proportional to the intensity or amplitudeof the received electromagnetic wave. Thus, the receive antennas 506,508 receive an electromagnetic wave from the outputs 502, 504,respectively, and generate an analog voltage based on the receivedelectromagnetic wave.

FIG. 5b shows another example of an electromagnetic coupler, which is amagic tee coupler 510. The magic tee coupler 510 is configured toreceive electromagnetic waves from the exit passages 108 b, 108 b aftertravel through the gas cells 104 a, 104 b. The magic tee coupler 510includes a first input RX1 coupled to the exit passage 108 a of the gascell 104 a and a second input RX2 coupled to the exit passage 108 b ofthe gas cell 104 b. The magic tee coupler 810 also includes a firstoutput 512 and a second output 514. In this example, the first output512 produces an electromagnetic wave that corresponds to the differenceof the first input RX1 and the second input RX2 (e.g., RX1−RX2), whilethe second output 514 produces an electromagnetic wave that correspondsto the sum of the first input RX1 and the second input RX1 (e.g.,RX1+RX2).

The first output 512 is coupled to a receive antenna 516, while thesecond output 514 is coupled to a receive antenna 518. The receiveantennas 516, 518 are functionally similar to the receive antennas 204a, 204 b, described above, and thus are configured to produce an outputsignal, for example, that is proportional to the intensity or amplitudeof the received electromagnetic wave. Thus, the receive antennas 516,518 receive an electromagnetic wave from the outputs 512, 514,respectively, and generate an analog voltage based on the receivedelectromagnetic wave.

Regardless of whether a rat-race coupler 500 or a magic tee coupler 510is utilized, one of the outputs of the coupler 500, 510 corresponds tothe difference between the electromagnetic waves after travel throughthe gas cells 104 a, 104 b. Thus, a single receive antenna may beutilized (e.g., with the output 502, 512 corresponding to the differencebetween the received electromagnetic waves), rather than the two receiveantennas 204 a, 204 b shown above with respect to FIG. 2, in which theprocessor 116 calculates the background-free signal based on thedifference in signals corresponding to the electromagnetic waves aftertravel through the gas cells 104 a, 104 b.

In certain examples of this description, various configurations ofreceive antennas are employed in conjunction with the processor 116 todetermine a difference between the electromagnetic waves after travelthrough the gas cell 104 a that contains the dipolar gas and the gascell 104 b that does not contain the dipolar gas. FIGS. 6a-6c showexamples of such configurations. In FIG. 6a , the configuration showncorresponds to FIG. 2, described above. For example, the receive antennaconfiguration 600 of FIG. 6a includes receive antennas 204 a, 204 b,which receive electromagnetic waves from the exit passages 108 a, 108 bafter travel through the gas cells 104 a, 104 b, respectively. In someexamples, an ADC 602 a, 602 b is coupled to each receive antenna 204 a,204 b, respectively, and receives the output signal from the receiveantenna 204 a, 204 b and converts the output signal to a digital signal,which is then provided to the processor 116. In other examples, theprocessor 116 itself includes integrated ADCs that are coupled to thereceive antennas 204 a, 204 b. In this example, since each output signalcorresponds to the absorption or transmission characteristic of one ofthe gas cells 104 a, 104 b, the processor 116 is configured to calculatea background-free signal based on the difference between the receivedsignals, such as described above with respect to FIGS. 3a-3c . In someexamples, the processor 116 is further configured to calculate anormalized, background-free signal based on the difference between thereceived signals and a sum of the received signals. For example, anormalized, background-free signal may be given by:(RX₁−RX₂)/(RX₁+RX₂)The background-free signal (or normalized, background-free signal) isprovided by the processor 116 to be utilized by the transceiver 110 togenerate the precision clock signal REFCLK as described above.

FIG. 6b shows another example of a receive antenna configuration 610,which is utilized with an electromagnetic coupler such as thosedescribed above with respect to FIGS. 5a and 5b . In FIG. 6b , a singlereceive antenna 612 is coupled to the output of the electromagneticcoupler that corresponds to the difference of the input electromagneticwaves after travel through the gas cells 104 a, 104 b (e.g., RX1−RX2, orthe output 506 of the rat-race coupler 500, or the output 516 of themagic tee coupler 510). The receive antenna 612 is functionally similarto the receive antennas 204 a, 204 b, described above. In one example,an ADC 614 is coupled to the receive antenna 612 and receives the outputsignal from the receive antenna 612 (e.g., an analog voltage) andconverts the output signal to a digital signal, which is then providedto the processor 116. In this example, since the input to the receiveantenna 612 already corresponds to the difference of the inputelectromagnetic waves after travel through the gas cells 104 a, 104 b,the processor 116 is configured to calculate a background-free signalbased on the signal received from the receive antenna. Thebackground-free signal is provided by the processor 116 to be utilizedby the transceiver 110 to generate the precision clock signal REFCLK asdescribed above. The processor 116 may additionally determine a maximumabsorption frequency based on the background-free signal, which in turnenhances the accuracy and stability of the REFCLK signal that resultsfrom such determination.

FIG. 6c shows another example of a receive antenna configuration 620,which is utilized with an electromagnetic coupler such as thosedescribed above with respect to FIGS. 5a and 5b . In FIG. 6c , a receiveantenna 622 is coupled to the output of the electromagnetic coupler thatcorresponds to the difference of the input electromagnetic waves aftertravel through the gas cells 104 a, 104 b (e.g., RX1−RX2, or the output506 of the rat-race coupler 500, or the output 516 of the magic teecoupler 510). Additionally, a receive antenna 624 is coupled to theoutput of the electromagnetic coupler that corresponds to the sum of theinput electromagnetic waves after travel through the gas cells 104 a,104 b (e.g., RX1+RX2, or the output 508 of the rat-race coupler 500, orthe output 518 of the magic tee coupler 510), which enables the exampletwo-receiver system 620 to calculate a normalized, background-freesignal. As described above, a normalized, background-free signal may begiven by: (RX₁−RX₂)/(RX₁+RX₂). The receive antennas 622, 624 arefunctionally similar to the receive antennas 204 a, 204 b, describedabove. In one example, an ADC 626, is coupled to the output of thereceive antenna 622 and an ADC 628 is coupled to the output of thereceive antenna 624 and receives the output signal from the receiveantennas 622, 624 (e.g., an analog voltage) and converts the outputsignal to a digital signal, which is then provided to the processor 116.The processor 116 is configured to calculate the normalized,background-free signal based on the signals generated by the receiveantennas 622, 624. The normalized, background-free signal is provided bythe processor 116 to be utilized by the transceiver 110 to generate theprecision clock signal REFCLK as described above. The processor 116 mayadditionally determine a maximum absorption frequency based on thenormalized, background-free signal, which in turn enhances the accuracyand stability of the REFCLK signal that results from such determination.

FIG. 7 shows a flow chart of a method 700 in accordance with examples ofthis description. The method 700 begins in block 702 with providing afirst electromagnetic wave to travel in a sealed interior waveguide of afirst gas cell. The method 700 then continues in block 704 withproviding a second electromagnetic wave to travel in a sealed interiorwaveguide of a second gas cell. For example, as described above, anelectromagnetic wave is provided to the gas cells 104 a, 104 b bytransmit antennas 202 a, 202 b by way of entry passages 106 a, 106 b.

The method 700 continues further in block 706 with receiving the firstand second electromagnetic waves after travel through the first andsecond gas cells. For example, after the signals pass through the gascells 104 a, 104 b, they are received by the receive antennas 204 a, 204b, respectively. As described above, the receive antennas 204 a, 204 breceive the electromagnetic waves and generate a signal in response tothe received electromagnetic wave, such as an analog voltage. In anotherexample, an electromagnetic coupler (e.g., a rat-race coupler 500 or amagic tee coupler 510 as described above with respect to FIGS. 5a and 5b) receives the electromagnetic wave after travel through the gas cells104 a, 104 b and generates at least one output that is then received bya receive antenna.

As described above, one gas cell contains a dipolar gas (e.g., 104 a),while the other gas cell does not contain a dipolar gas (e.g., 104 b).The response of the gas cell not containing the dipolar gas 104 b toelectromagnetic wave interrogation is generally a background frequencyresponse, while the response of the gas cell containing the dipolar gas104 a to electromagnetic wave interrogation also includes the quantumresponse of the dipolar gas as a function of the wave frequency. Thedifferences in frequency response between the gas cells 104 a, 104 b maybe leveraged to determine a background-free response. For example, themethod 700 continues in block 708 with generating a background-freesignal based on a difference between the first and secondelectromagnetic waves. In the example where receive antennas 204 a, 204b receive the electromagnetic waves (and generate a signal in response),the processor 116 calculates the background-free signal based on thedifference in signals corresponding to the electromagnetic waves aftertravel through the gas cells 104 a, 104 b. In examples where anelectromagnetic coupler is utilized, one of the outputs of the couplercorresponds to the difference between the electromagnetic waves aftertravel through the gas cells 104 a, 104 b, and thus generates thebackground-free signal.

In addition to the foregoing, which improves the accuracy and stabilityof a precision clock source by reducing or eliminating the backgroundresponse of the system from the analyzed quantum response of a dipolargas, other examples additionally address Doppler broadening caused bymolecules of dipolar gas having a velocity relative to the direction ofelectromagnetic wave propagation.

For example, the Allan deviation (which is the square root of the Allanvariance) is a measure of frequency stability of clock signals (e.g., inclocks, oscillators, amplifiers), and in effect is a measure offrequency distribution over a number of samples. As a result, the lowerthe Allan deviation measure, the lower the variance of distribution andthe better the performance of the clock signal. Further, the Allandeviation is inversely proportional to both the quality factor (Q) andsignal-to-noise ratio (SNR) of the frequency response curve of thetransceiver 110 in an example, as it processes the received RX signalresponse to detect an absorption peak frequency. By increasing one orboth of the Q and SNR of the system, the Allan deviation measure isimproved. Reducing the pressure in the gas cell 104 a, 104 b achievescertain improvements in the Allan deviation, as this pressure reductionreduces the width of the transition caused by pressure broadeningphenomena. However, Q is only improved down to a certain pressure, whilefor pressures below a certain value (e.g., 0.1 mbar), the width cannotbe reduced further because of Doppler broadening, which is independentof pressure and mostly dependent on the temperature of the gas. Pressurereduction also reduces the number of molecules available forinterrogation and thus the amplitude of the quantum transition signal.An optimum pressure can be identified (for OCS this pressure isapproximately 0.1 mbar) where the Allan deviation can be minimized byhaving the minimum transition width possible and the maximum amplitudepossible.

As described above, existing systems can be susceptible to Dopplerbroadening, which is caused by the distribution of velocities ofatoms/molecules, particularly in response to higher temperatures.Particularly, for atoms having velocities in a same direction as thedirection of propagation of the electromagnetic wave, the Doppler effectwill cause the transition of the dipolar molecules from the lower energyvibrational state to the higher energy vibrational state to occur whenthe frequency of the electromagnetic signal is lower than the frequencythat corresponds to the energy difference of the two vibrational states(e.g., 182.427 GHz for OCS), and conversely, for atoms having velocitiesin an opposing direction as the prior art unidirectional signal, theDoppler effect will cause the rotational transition of those atoms tooccur at an excitation frequency that is higher than the intrinsicquantum rotational state transition frequency for the dipole. Thus, theresult of Doppler broadening is a wider spectral line when interrogatingthese atoms/molecules, which accordingly provides less accuracy inidentifying a particular frequency of quantum transition.

Examples of this description address the foregoing by providing two gascells containing a dipolar gas. One of the gas cells is coupled to twotransmitters (or transmit antennas) to provide electromagnetic wavesthrough the gas cell in opposite directions, while the other gas cell iscoupled to one transmitter (or transmit antenna) to provide anelectromagnetic wave through the gas cell in one direction. The responseto electromagnetic wave interrogation of the gas cell that receives anelectromagnetic wave in one direction is generally similar to the gascell containing the dipolar gas described above, and includes thequantum response of the gas as a function of the wave frequency,containing a peak at the frequency where maximum absorption by thedipolar gas of the electromagnetic wave occurs. However, the response toelectromagnetic wave interrogation of the gas cell that receiveselectromagnetic waves in opposite directions is a Doppler-free response,which is described in greater detail below. As described above, the gascells are substantially similar in their physical characteristics, suchas dimensions, shape, manufacturing processes, interior coatings,entry/exit passage construction, and the like, such that the response ofeach gas cell includes approximately the same background response inaddition to the quantum response (both Doppler-induced and Doppler-free)of the gas.

The response of the gas cell that receives an electromagnetic wave inone direction is subtracted from the response of the gas cell thatreceives electromagnetic waves in opposite directions (or vice versa).As described further below, a processor or an electromagnetic couplercarries out such subtraction. As a result, the background andDoppler-induced responses are effectively removed, and a resultingsignal is indicative of a background- and Doppler-free quantum responseof the gas. The background- and Doppler-free quantum response isutilized by a transceiver to generate a precision clock signal (e.g.,REFCLK) with improved accuracy and stability due to the Doppler-freenature of the response, and additionally without being colored by thebackground frequency response of the various system components.

FIG. 8 shows a block diagram of a system 800, which in one example is aclock system. The system 800 includes a semiconductor substrate 802including a first gas cell 804 a and a second gas cell 804 b. The firstand second gas cells 804 a, 804 b each include a first passage 806 a,806 b, respectively, which serves as an entrance into the gas cell 804a, 804 b. The first gas cell 804 a also includes a second passage 807that serves as a second entrance into the gas cell 804 a, so thatelectromagnetic waves may be provided to the gas cell 804 a in oppositedirections. The first and second gas cells 804 a, 804 b also eachinclude a passage 808 a, 808 b, respectively, which serves as an exitfrom the gas cell 804 a, 804 b. In this example, the exit passages 808a, 808 b are located in an additional cavity portion of the gas cells804 a, 804 b that departs away from a linear portion of the gas cells804 a, 804 b.

In one example, the gas cells 804 a, 804 b are formed in connection withan integrated circuit wafer, which can include multiple layers affixedrelative to the semiconductor substrate 802. As described above, gascells 804 a, 804 b include a sealed enclosure having an interior inwhich a dipolar gas is stored at a relatively low (e.g., 0.1 mbar)pressure.

In one example, the gas cells 804 a, 804 b also include, or are linedalong most of their interior surfaces with, a material to facilitate theinterior as a signal waveguide, where such material is, for example, aconductor or a dielectric. In an example, the cross-sectional shape ofgas cells 104 a, 104 b is square, rectangular, trapezoidal, or othershapes, while the dimensions of gas cells 804 a, 804 b may vary, wherethe gas cells 804 a, 804 b are 30 to 150 mm long, 1 to 3 mm wide, and0.5 to 1.5 mm tall, where selecting these or comparable sizes matchesproperties for efficient wave propagation given the frequency of thedesired wave. Further, while the longitudinal shape is linear in FIG. 8(and other figures), it also may bend or turn so as to form, forexample, a meandering path.

A transceiver 110 (e.g., similar in function to the transceiver 110described above with respect to FIGS. 1 and 2) is coupled to the gascells 804 a, 804 b and is configured to provide an electromagnetic waveto a directional coupler 803, which receives the electromagnetic waveand divides the power of the received electromagnetic wave into twoelectromagnetic waves as outputs. The directional coupler 803 providesone of its outputs to a transmit pump antenna 813 and the other of itsoutputs to a second directional coupler 805. The second directionalcoupler 805 is similar in function to the directional coupler 803, andprovides one of its outputs to transmit probe antenna 812 a and theother of its outputs to transmit probe antenna 812 b. In an example, thepower provided to the transmit pump antenna 813 is greater than thepower provided to the transmit probe antennas 812 a, 812 b, while thepower provided to the transmit probe antennas 812 a, 812 b isapproximately equal. For example, the directional coupler 803 provides90% of the received electromagnetic wave power to the transmit pumpantenna 813 and the remaining 10% of the received electromagnetic wavepower to the directional coupler 805. The directional coupler 805 thenprovides approximately 50% of the received electromagnetic wave power(or 5% of the power provided to the directional coupler 803) to each ofthe transmit probe antennas 812 a, 812 b.

The transceiver 110 is coupled through the directional couplers 803, 805to the gas cells 804 a, 804 b by way of their respective entry passages806 a, 806 b, 807. The transceiver 110 is also coupled to the gas cells804 a, 804 b and is configured to receive the electromagnetic wavesafter travel through the gas cells 804 a, 804 b by way of theirrespective exit passages 808 a, 808 b.

For example, the transmit probe antennas 812 a, 812 b are positionedproximate the entry passages 806 a, 806 b, so that electromagneticenergy from the transceiver 110, through directional couplers 803, 805,may be communicated to the transmit probe antennas 812 a, 812 b and theninto the gas cells 804 a, 804 b by way of entry passages 806 a, 806 b.Additionally, the transmit pump antenna 813 is positioned proximate theentry passage 807, so that electromagnetic energy from the transceiver110, through directional coupler 803, maybe communicated to the transmitpump antenna 813 and then into the gas cell 804 a, in a directionopposite the electromagnetic energy provided by the transmit probeantenna 806 a. As described in further detail below, in one example, aseparate transmitter or transceiver 110 (not shown in FIG. 8 forsimplicity) provides the electromagnetic energy/wave to each of the gascells 804 a, 804 b (e.g., by way of transmit probe antennas 812 a, 812 band transmit pump antenna 813). In another example, a single transmitteror transceiver 110 provides the electromagnetic energy/wave, which isdivided by the directional couplers 803, 805 as described above.

The transceiver 110 is similar to the transceiver 110 described above,and is both for transmitting (TX) and receiving (RX) signals. Thetransceiver 110 generally provides a controlled TX signal that is sweptacross a particular frequency range from below to past the intrinsicquantum rotational state transition frequency for the dipolar gas in thegas cells 804 a, 804 b (e.g., 182.427 GHz for OCS). After the signalpasses through the gas cell, it is received by the transceiver 110coupled to receive the RX signal from receive antennas 814 a, 814 b.Particularly, receive antennas 814 a, 814 b are positioned proximate theexit passages 808 a, 808 b of the gas cells 804 a, 804 b, so thatelectromagnetic energy that travels through gas cells 804 a, 804 b maybe communicated from the exit passages 808 a, 808 b to receive antennas814 a, 814 b and then to transceiver 110. Although not shownschematically, in some examples the receive antennas 804 a, 804 binclude a square-law detector or another type of detector that producean output signal, for example, that is proportional to the intensity oramplitude of the received electromagnetic wave are coupled to theantennas 804 a, 804 b. Thus, in such examples, the receive antennas 804a, 804 b receive an electromagnetic wave from the exit passages 808 a,808 b and generate an analog voltage based on the receivedelectromagnetic wave. Further, although shown schematically as separatecomponents, it should be appreciated that in some examples thetransceiver 110 (or separate transmitters and receivers, as the case maybe) includes (e.g., as integrated devices) the associated antennas 812a, 812 b, 813, 814 a, 814 b (including square-law detectors as describedabove).

Similar to above in FIGS. 5a, 5b, and 6a-6c , in one example, a separatereceive antenna 814 a, 814 b receives the electromagnetic energy/waveafter travel through each of the gas cells 804 a, 804 b. The receiveantennas 814 a, 814 b convert the electromagnetic wave into an RXsignal, such as an analog voltage, which is further processed by theprocessor 116 before being utilized by the transceiver 110. In anotherexample, an electromagnetic coupler similar to those shown in FIGS. 5aand 5b receives and processes the electromagnetic energy/waves aftertravel through each of the gas cells 804 a, 804 b (e.g., in theelectromagnetic domain), while one or more receive antennas receive theresultant processed electromagnetic wave from the electromagneticcoupler, convert the processed electromagnetic wave into an RX signal,such as an analog voltage, which is utilized by the transceiver 110.

As described above, a processor 116 is coupled to the transceiver 110and is configured to, among other things, control the transceiver 110 toprovide electromagnetic waves to the gas cells 804 a, 804 b and processsignals received from the gas cells 804 a, 804 b and provide suchprocessed signals to the transceiver 110. The transceiver 110 isconfigured to provide a stable reference clock signal in response toelectromagnetic interrogation of the gas cells 804 a, 804 b, which isdescribed in further detail below.

As described above, one or more of the transceiver 110, the gas cells804 a, 804 b, and associated circuitry and electronic devices such asthe processor 116 may add to or color the frequency response observed atthe transceiver 110 and processed by the processor 116, which affectsthe accuracy of the determined quantum response of the gas, and thus theaccuracy of the atomic clock as a precision clock source. Additionally,Doppler broadening results in a wider spectral line when interrogatingthe dipolar gas (or other atoms/molecules), which accordingly providesless accuracy in identifying a particular frequency of the quantumtransition, further affecting the accuracy and stability of the atomicclock as a precision clock source. Examples of this description addressthe foregoing by subtracting the response of the gas cell 804 b thatreceives an electromagnetic wave in one direction from the response ofthe gas cell 804 a that receives electromagnetic waves in oppositedirections (or vice versa). As a result, the background andDoppler-induced responses are effectively removed, and a resultingsignal is indicative of a background- and Doppler-free quantum responseof the gas. The background- and Doppler-free quantum response isutilized by the transceiver 110 to generate the precision clock signalREFCLK with improved accuracy and stability due to the Doppler-freenature of the response, and additionally without being colored by thebackground frequency response of the various system components. Variousexamples of this approach are described in further detail below.

Generally, the following refers to feedback control between theprocessor 116 and the transceiver 110. However, in certain examples, thetransceiver 110 may provide feedback control independently of theprocessor 116. For example, the transceiver 110 sweeps the modulatedbase frequency TX signal such that the base frequency is swept across aninitial frequency range that includes the intrinsic quantum rotationalstate transition frequency for the dipolar gas in gas cells 804 a, 804b. Thus, in the example where the dipolar gas is OCS, the range willinclude the intrinsic quantum rotational state transition frequency of182.427 GHz for OCS, and could include, for example, a sweep from 182.25GHz to 182.75 GHz. Thus, the TX signal delivers an energy E todirectional coupler 803, sweeping across this frequency range, so thatthe same frequency is simultaneously applied by both the transmit pumpantenna 813 and the transmit probe antennas 812 a, 812 b. As a result,bidirectional propagation in opposite directions is accomplished for thegas cell 804 a, while unidirectional propagation in one direction isaccomplished for the gas cell 804 b. In one example, while the TX signalrepresents a certain amount of energy E, the directional coupler 803couples a first amount E1 of that energy to the directional coupler 805and a second amount E2 of that energy (e.g., subject to possible signalloss TX−E1=E2) to the transmit pump antenna 813. Preferably E2>E1, wherefor example E2 may be 90% of TX, leaving 10% of TX as E1. Thedirectional coupler 805 provides approximately equal energy (e.g.,0.5*E1) to each of the transmit probe antennas 812 a, 812 b.

The different transmitter examples described above with respect to FIG.4a also apply to the example of FIG. 8, in which a background- andDoppler-free quantum response of gas is determined. For example, afirst, second, and third transmitter (or transmit portions of first,second, and third transceivers) are coupled to the entry passages 806 a,807, 806 b, respectively (e.g., by transmit antennas 812 a, 813, 812 b,respectively). In this example, the processor 116 (or other transmitterand/or transceiver circuitry) may be configured to cause the first andthird transmitters to generate approximately equal electromagnetic wavesto the first and second gas cells 804 a, 804 b, respectively, and tocause the second transmitter to generate an electromagnetic wave to thefirst gas cell 804 a in direction opposite the first transmitter. In anexample, the second transmitter generates an electromagnetic wave havinga greater amount of energy than those generated by the first and thirdtransmitters.

FIG. 9a shows a set of waveforms 900 of example signals generated by areceiver or the transceiver 110 in response to the electromagneticenergy received from the exit passages 808 a, 808 b of the gas cells 804a, 804 b. For example, the waveform 902 shows transmission energy as afunction of frequency of the received electromagnetic wave from the gascell 804 b, which is Doppler-broadened as described above, due to theunidirectional propagation of the electromagnetic wave in the gas cell804 b. The waveform 904 shows transmission energy as a function offrequency of the received electromagnetic wave from the gas cell 804 a,which is Doppler-free due to the bidirectional propagation of theelectromagnetic waves in the gas cell 804 a, which is described infurther detail below. The waveform 906 shows an example backgroundsignal, similar to that described above with respect to the systems ofFIGS. 1 and 2, which is present in both the waveform 902 and 904, andthus is superimposed on those portions of the waveforms 902 and 904 thatdemonstrate the background response.

FIG. 9b shows a portion 901 of FIG. 9a in zoomed in detail, and alsoincludes the Doppler-broadened signal waveform 902 (from gas cell 804b), the Doppler-free waveform 904 (from gas cell 804 a), and thebackground signal waveform 906. The Doppler-broadened signal waveform902 is similar to the absorption waveform described above with respectto FIG. 4 and, indeed, the gas cell 804 b is generally similar infunction to the gas cell 104 b with exception for particular geometricdifferences. However, the bidirectional propagation of electromagneticwaves in opposite directions in the gas cell 804 a results in aDoppler-free signal received by the receive antenna 814 a from the exitpassage 808 a.

The transmit probe antenna 812 a and transmit pump antenna 813 transmitat the same frequency, and that frequency is swept across a range thatincludes the intrinsic quantum rotational state transition frequency forthe dipole (e.g., 182.427 GHz for OCS). Generally, therefore, thesweeping of frequency may be low to high (or high to low), producing theresponse shape depicted in FIG. 9b as waveform 904. Note that whileFIGS. 9a and 9b plot transmission, absorption could be equivalentlyanalyzed. In any event, as the swept frequency approaches the intrinsicquantum rotational state transition frequency, the transmission ofenergy through the dipolar gas decreases as shown, and as detected inthe RX signal, creates an absorption spectra that is flatter away fromthat intrinsic frequency and that ascends from both directions as thefrequency sweep nears the dipolar gas intrinsic frequency. Additionally,as the intrinsic frequency is approached, a first peak 922 occurs whichis shown as a minimum in terms of energy transmission and at a frequencybelow the Doppler free frequency 924, and similarly above the Dopplerfree frequency 924 a second peak 926 occurs. As further detailed below,however, example embodiments are able to detect an additional peak asthe Doppler free frequency 924, between peaks 922 and 926.

Regarding the Doppler-free response of the gas cell 804 a, in an exampleone of the bidirectional TX signals is provided at a higher energy thanthe other by virtue of the directional coupler 803, where for sake ofconvention in other technologies the higher-energized signal is termedthe pump. As a result, most of the atoms/molecules interrogated by thehigher-energized signal from the transmit pump antenna 813, at theappropriate quantum frequency, will be excited to an energy level higherthan a lower energy (e.g., ground) state, while other of theatoms/molecules will remain at the lower energy state. Thus in responseto the signal from the transmit probe antenna 812 a, the number ofmolecules that are in the ground state is significantly reduced becausemost of them have been excited to the excited state by the transmit pumpantenna 813 signal causing a decrease in the absorption profile, or anincrease in the transmission profile.

In addition, the bidirectional or counter-propagating nature of theprobe (813) and pump (812 a) signals also reduces or eliminates theDoppler effect. Particularly, atoms/molecules at zero velocity do notdemonstrate or experience the Doppler effect, and are accordinglyaffected by the frequency aspect of both of the counter-propagatingwaves, where again the pump (813) signal has depopulated a portion ofthe ground state to the higher energy state. As a result of thepreceding, fewer of the ground state atoms remain at the Doppler-freefrequency 924, so there are fewer atoms to absorb the probe (812 a)energy and a corresponding drop in absorption, where such lack ofabsorption of that probe (812 a) energy is evident in the resultant RXplot of FIG. 9b , which includes an increase in transmission energycentered around the intrinsic frequency 924, the increase intransmission arising from the fewer low-energy atoms to absorb the probe(812 a) signal, which is the signal received by the receive antenna 814a. Thus, the gas cell 804 a provides so-called Doppler-freespectroscopy, in that Doppler broadening is no longer an issue underthis approach. In some examples, the Doppler-free benefits may berealized independently of the gas pressure in the gas cell 804 a.

Further, the frequency width between peaks 922 and 926, DP is less thanthe frequency width ΔfO of the outer Gaussian descending portions of theplot. As a result, the Q relative to the frequency width ΔfDP isconsiderably better than the Q relative to the frequency width ΔfO ofthe outer descending portions. Accordingly, the improved Q of theDoppler free architecture improves the Allan deviation of system 800(and the other comparable systems described herein).

FIG. 9c shows a waveform 950 of an example Doppler-free, background-freesignal that results when the Doppler-broadened waveform 902 (e.g.,obtained from the receive antenna 814 b coupled to the gas cell 804 bthat experiences only unidirectional propagation of the electromagneticwave) is subtracted from the Doppler-free waveform 904 (e.g., obtainedfrom the receive antenna 814 a coupled to the gas cell 804 a thatexperiences bidirectional propagation of electromagnetic waves inopposite directions as described above). As described in further detailbelow, in some examples the processor 116 is configured to receive theDoppler-broadened signal (e.g., waveform 902) and the Doppler-freesignal (e.g., waveform 904) and calculates the difference represented bythe waveform 950. In other examples, as described above with respect toFIGS. 5a, 5b, 6b , and 6 c, an electromagnetic coupler is utilized thatreceives the electromagnetic waves after travel through the gas cells804 a, 804 b and generates a resulting electromagnetic wave that isindicative of the difference in the received waves. Thus, theDoppler-free and background-free waveform 950 represents suppression ofthe impacts of gas cell 804 geometry, environment, or surroundingelectronics like the transmitter or transceiver 110, in addition to theDoppler broadening effect described above, which increases the accuracyof determining the maximum absorption frequency and thus the accuracyand stability of the REFCLK signal that results from such determination.

FIG. 10 shows a flow chart of another method 1000 in accordance withexamples of this description. The method 1000 begins in block 1002 withproviding a first electromagnetic wave to travel in a sealed interiorwaveguide of a first gas cell along a first direction. The method 1000continues in block 1004 with providing a second electromagnetic wave totravel in the sealed interior of the first gas cell along a seconddirection opposite the first direction. For example, as described above,an electromagnetic wave is provided to the gas cell 804 a by thetransmit probe antenna 812 a positioned proximate the entry passage 806a. Additionally, an electromagnetic wave is provided to the gas cell 804a by the transmit pump antenna 813 positioned proximate the entrypassage 807. Thus, electromagnetic energy is communicated to thetransmit pump antenna 813 and then into the gas cell 804 a, in adirection opposite the electromagnetic energy provided by the transmitprobe antenna 806 a. The method 1000 continues in block 1006 withproviding a third electromagnetic wave to travel in a sealed interiorwaveguide of a second gas cell. For example, as described above, anelectromagnetic wave is provided to the gas cell 804 b by the transmitprobe antenna 812 b positioned proximate the entry passage 806 b.

The method 1000 continues further in block 1008 with receiving the firstand third electromagnetic waves after travel through the first andsecond gas cells. For example, after the signals from the transit probeantennas 806 a, 806 b pass through the gas cells 804 a, 804 b, they arereceived by the receive antennas 808 a, 808 b, respectively. Asdescribed above, the receive antennas 808 a, 808 b receive theelectromagnetic waves and generate a signal in response to the receivedelectromagnetic wave, such as an analog voltage. In another example, anelectromagnetic coupler (e.g., a rat-race coupler 500 or a magic teecoupler 510 as described above with respect to FIGS. 5a and 5b )receives the electromagnetic wave from the transit probe antennas 806 a,806 b after travel through the gas cells 804 a, 804 b and generates atleast one output that is then received by a receive antenna.

Finally, the method 1000 continues in block 1010 with generating abackground-free signal based on a difference between the first and thirdelectromagnetic waves. As described above, one or more of thetransceiver 110, the gas cells 804 a, 804 b, and associated circuitryand electronic devices such as the processor 116 may add to or color thefrequency response observed at the transceiver 110 and processed by theprocessor 116, which affects the accuracy of the determined quantumresponse of the gas, and thus the accuracy of the atomic clock as aprecision clock source. Additionally, Doppler broadening results in lessaccuracy in identifying a particular frequency of the quantumtransition, further affecting the accuracy and stability of the atomicclock as a precision clock source. Thus, in one example, the processor116 calculates the background-free signal based on the difference in theresponse of the gas cell 804 b that receives an electromagnetic wave inone direction and the response of the gas cell 804 a that receiveselectromagnetic waves in opposite directions (or vice versa). Inexamples where an electromagnetic coupler is utilized, one of theoutputs of the coupler corresponds to the difference between theelectromagnetic waves after travel through the gas cells 804 a, 804 b,and thus generates the background-free signal. As a result, thebackground and Doppler-induced responses are effectively removed, and aresulting signal is indicative of a background- and Doppler-free quantumresponse of the gas.

In this description, the term “couple” or “couples” means either anindirect or direct connection. Thus, if a first device couples to asecond device, that connection may be through a direct connection orthrough an indirect connection via other devices and connections.Similarly, a device that is coupled between a first component orlocation and a second component or location may be through a directconnection or through an indirect connection via other devices andconnections. Also, in this description, an element or feature that is“configured to” perform a task or function may be configured (e.g.,programmed or structurally designed) at a time of manufacturing by amanufacturer to perform the function and/or may be configurable (orre-configurable) by a user after manufacturing to perform the functionand/or other additional or alternative functions. The configuring may bethrough firmware and/or software programming of the device, through aconstruction and/or layout of hardware components and interconnectionsof the device, or a combination thereof. Further, uses of the phrases“ground” or similar in this description include a chassis ground, anEarth ground, a floating ground, a virtual ground, a digital ground, acommon ground, and/or any other form of ground connection applicable to,or suitable for, the teachings of this description. Unless otherwisestated, in this description, “about,” “approximately,” or“substantially” preceding a value means +/−10 percent of the statedvalue.

Modifications are possible in the described embodiments, and otherembodiments are possible, within the scope of the claims.

What is claimed is:
 1. A system, comprising: a first gas cell comprisinga sealed interior waveguide that contains a dipolar gas; a second gascell comprising a sealed interior waveguide that does not contain adipolar gas; a first transmit antenna coupled to the first gas cell andconfigured to provide a first electromagnetic wave to travel in thesealed interior of the first gas cell; a second transmit antenna coupledto the second gas cell and configured to provide a secondelectromagnetic wave to travel in the sealed interior of the second gascell; a first receive antenna coupled to the first gas cell andconfigured to provide a first signal indicative of an amount of energyin the first electromagnetic wave after travel through the first gascell; a second receive antenna coupled to the second gas cell andconfigured to provide a second signal indicative of an amount of energyin the second electromagnetic wave after travel through the second gascell; a processor coupled to the first and second receive antennas andconfigured to provide at a processor output a background-free signalthat is a difference between the first signal and the second signal. 2.The system of claim 1, further comprising: a first transmitter coupledto the first transmit antenna, the first transmitter configured togenerate the first electromagnetic wave; and a second transmittercoupled to the second transmit antenna, the second transmitterconfigured to generate the second electromagnetic wave; wherein thefirst and second transmitters are configured to provide approximatelyequal electromagnetic waves to the first and second transmit antennas,respectively.
 3. The system of claim 1, further comprising: atransmitter configured to generate an electromagnetic wave; and adirectional coupler coupled to the transmitter and to the first andsecond transmit antennas, the directional coupler configured to receivethe electromagnetic wave from the transmitter and generate the first andsecond electromagnetic waves, wherein the first and secondelectromagnetic waves are approximately equal.
 4. The system of claim 1,wherein the first and second signals comprise analog signals, the systemfurther comprising an analog-to-digital converter (ADC) coupled to thereceive antennas and to the processor, the ADC configured to: convertthe first signal to a first digital signal; convert the second signal toa second digital signal; and provide the first and second digitalsignals to the processor.
 5. The system of claim 1, wherein the firstand second gas cells are formed using one or more layers of asemiconductor wafer.
 6. The system of claim 1, wherein the first andsecond gas cells are formed using approximately equal dimensions.
 7. Thesystem of claim 1, wherein the processor is further configured tocalculate a normalized, background-free signal based on the differencebetween the first signal and the second signal and on a sum of the firstsignal and the second signal.
 8. A system, comprising: a first gas cellcomprising a sealed interior waveguide that contains a dipolar gas; asecond gas cell comprising a sealed interior waveguide that does notcontain a dipolar gas; a first transmit antenna coupled to the first gascell and configured to provide a first electromagnetic wave to travel inthe sealed interior of the first gas cell; a second transmit antennacoupled to the second gas cell and configured to provide a secondelectromagnetic wave to travel in the sealed interior of the second gascell; and an electromagnetic coupler coupled to the gas cells andconfigured to: receive the first and second electromagnetic waves aftertravel through the first and second gas cells; and provide anelectromagnetic wave indicative of a difference between the first andsecond electromagnetic waves.
 9. The system of claim 8, furthercomprising a receive antenna coupled to the electromagnetic coupler andconfigured to provide a first signal indicative of an amount of energyin the electromagnetic wave indicative of the difference.
 10. The systemof claim 8, wherein the electromagnetic coupler is further configured toprovide an electromagnetic wave indicative of a sum of the receivedfirst and second electromagnetic waves.
 11. The system of claim 10,further comprising: a first receive antenna coupled to theelectromagnetic coupler and configured to provide a first signalindicative of an amount of energy in the electromagnetic wave indicativeof the difference; and a second receive antenna coupled to theelectromagnetic coupler and configured to provide a second signalindicative of an amount of energy in the electromagnetic wave indicativeof the sum.
 12. The system of claim 11, further comprising a processorcoupled to the first and second receive antennas and configured tocalculate a normalized, background-free signal based on the first signaland the second signal.
 13. The system of claim 8, wherein the couplercomprises a rat race coupler.
 14. The system of claim 8, wherein thecoupler comprises a magic tee coupler.
 15. The system of claim 8,further comprising: a processor; a first transmitter coupled to thefirst transmit antenna, the first transmitter configured to provide thefirst electromagnetic wave; and a second transmitter coupled to thesecond transmit antenna, the second transmitter configured to providethe second electromagnetic wave; wherein the first and secondtransmitters are configured to provide approximately equalelectromagnetic waves for the first and second gas cells, respectively.16. The system of claim 8, further comprising: a transmitter configuredto provide an electromagnetic wave; and a directional coupler coupled tothe transmitter and to the first and second transmit antennas, thedirectional coupler configured to receive the electromagnetic wave fromthe transmitter and generate the first and second electromagnetic waves,wherein the first and second electromagnetic waves are approximatelyequal.
 17. The system of claim 8, wherein the first and second gas cellsare formed using one or more layers of a semiconductor wafer.
 18. Thesystem of claim 8, wherein the first and second gas cells are formedusing approximately equal dimensions.
 19. A method, comprising:providing a first electromagnetic wave to travel in a sealed interiorwaveguide of a first gas cell; providing a second electromagnetic waveto travel in a sealed interior waveguide of a second gas cell; receivingthe first and second electromagnetic waves after travel through thefirst and second gas cells; and generating a background-free signalbased on a difference between the first and second electromagneticwaves; wherein the sealed interior of the first gas cell contains adipolar gas and the sealed interior of the second gas cell does notcontain a dipolar gas.